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I want a serious answer, here, because I can't think of a reason that doesn't stem from insecurity/control issues, but maybe there is one.

Red flag is right. Veto can only mean a couple of things:

1. I don't trust you because you are a child and cannot survive without my direct supervision
2. I am insecure and need to feel the illusion of power over your life in order to deal with my personal issues

None of this is fertile ground for having an adult intimate relationship.

This is your polyship, not mine. But you haven't "gotten into it" yet. You are kinda checking out the offer here, right? So... check it out thoroughly then.

It sounds like you have a plan -- meet the woman and ask what this is all about. So... meet her and ask?

And don't just ask why this is in place, could ask if this is a hard limit (will never change) or a soft limit (could change over time or change after X encounters). Maybe that makes a difference to you. Maybe there's some trauma story of her own there.

But if in the end you get some kind of answer and it still bugs ya? Step away and say "Thank you for your time. But this is not an offer I want to participate in." And walk away. The price of admission here is not to your liking.

Not every date is gonna be a long haul runner. *shrug* That is what dating is for -- to find the compatible ones.

I cross-posted this to reddit's /r/polyamory. My date was a redditor. He had his wife create a throwaway to respond to me. Long story short, they came at poly from the swinging/nonmonogamy side. This rule is a remnant of navigating poly from that end of things, apparently.

She says she's open to renegotiating it/cancelling it if everyone agrees, and that she's feeling compersion that I went out with him and liked him so much.

So, that's positive!

In return, I wrote her explaining why vetoes suck for me personally, and what I'm wary about, and the pitfalls these kinds of rules tend to fall into. I also mentioned that it was obviously her relationship and her rules, and that I respected it even if it wouldn't work for me. And that if she wasn't willing to compromise, I could bounce and wouldn't be offended.

they came at poly from the swinging/nonmonogamy side. This rule is a remnant of navigating poly from that end of things, apparently.

That certainly sounds like a potential point of growth. Hopefully if she dumps the VETO power it will be to grow emotionally - not just to sate the desires of the people around her. One would be a very good sign, the other would be a temporary reprieve with a difficulty to come at a later date.